The invention relates to the field of low-loss resonators.
Electromagnetic resonators spatially confine electromagnetic energy. Such resonators have been widely used in lasers, and as narrow-bandpass filters. A figure of merit of an electromagnetic resonator is the quality factor Q. The Q-factor measures the number of periods that electromagnetic fields can oscillate in a resonator before the power in the resonator significantly leaks out. Higher Q-factor implies lower losses. In many devices, such as in the narrow bandpass filtering applications, a high quality factor is typically desirable.
In order to construct an electromagnetic resonator, i.e., a cavity, it is necessary to provide reflection mechanisms in order to confine the electromagnetic fields within the resonator. These mechanisms include total-internal reflection, i.e. index confinement, photonic band gap effects in a photonic crystal, i.e., a periodic dielectric structure, or the use of metals. Some of these mechanisms, for example, a complete photonic bandgap, or a perfect conductor, provide complete confinement: incident electromagnetic wave can be completely reflected regardless of the incidence angle. Therefore, by surrounding a resonator, i.e., a cavity, in all three dimensions, with either a three-dimensional photonic crystal 100 with a complete photonic bandgap as shown in FIG. 1A, or a perfect conductor with minimal absorption losses, the resonant mode in the cavity can be completely isolated from the external world, resulting in a very large Q. In the case of a cavity embedded in a 3D photonic crystal with a complete bandgap, the Q in fact increases exponentially with the size of the photonic crystal.
Total internal reflection, or index confinement, on the other hand, is an incomplete confining mechanism. The electromagnetic wave is completely reflected only if the incidence angle is larger than a critical angle. Another example of an incomplete confining mechanism is a photonic crystal with an incomplete photonic bandgap. An incomplete photonic bandgap reflects electromagnetic wave propagating along some directions, while allowing transmissions of electromagnetic energy along other directions. If a resonator is constructed using these incomplete confining mechanisms, since a resonant mode is made up of a linear combination of components with all possible wavevectors, part of the electromagnetic energy will inevitably leak out into the surrounding media, resulting in an intrinsic loss of energy. Such a radiation loss defines the radiation Q, or intrinsic Q, of the resonator, which provides the upper limit for the achievable quality factor in a resonator structure.
In practice, many electromagnetic resonators employ an incomplete confining mechanism along at least one of the dimensions. Examples include disk, ring, or sphere resonators, distributed-feedback structures with a one-dimensional photonic band gap, and photonic crystal slab structures with a two-dimensional photonic band gap. In all these examples, light is confined in at least one of the directions with the use of index confinement.
The radiation properties of all these structures have been studied extensively and are summarized below.
In a disk 102, ring or sphere resonator (FIG. 1B), the electromagnetic energy is confined in all three dimensions by index confinement. Since index confinement provides an incomplete confining mechanism, the electromagnetic energy can leak out in all three dimensions. Many efforts have been reported in trying to tailor the radiation leakage from microdisk resonators. It has been shown that the radiation Q can be increased by the use of a large resonator structure that supports modes with a higher angular momentum, and by reducing the surface roughness of a resonator. Also, the use of an asymmetric resonator to tailor the far-field radiation pattern and decrease the radiation Q has been reported.
In a distributed-feedback cavity structure 104 as shown in FIG. 1C, or a one-dimensional photonic crystal structure, electromagnetic energy is confined in a hybrid fashion. Here, a cavity is formed by introducing a phase-shift, or a point defect into an otherwise perfectly periodic dielectric structure. The one-dimensional periodicity opens up a photonic band gap, which provides the mechanism to confine light along the direction of the periodicity. In the other two dimensions, the energy is confined with the use of index confinement. The leakage along the direction of the periodic index contrast can in principle be made arbitrarily small by increasing the number of periods on both sides of the cavity. This leakage is often termed butt loss, and is distinct from radiation loss. In the other two dimensions, however, light will be able to leak out. The energy loss along these two dimensions limits the radiation Q of the structure. Radiation Q of these structures have been analyzed by many. The radiation Q can be improved by increasing the index contrast between the cavity region and the surrounding media, by choosing the symmetry of the resonance mode to be odd rather than even, and by designing the size of the phase shift such that the resonance frequency is closer to the edge of the photonic band gap.
Similar to the distributed feedback structure, a photonic crystal slab structure 106 as shown in FIG. 1D employs both the index confinement and the photonic band gap effects. A photonic crystal slab is created by inducing a two-dimensionally periodic index contrast into a high-index guiding layer. A resonator in a photonic crystal slab can be created by breaking the periodicity in a local region to introduce a point defect. A point defect consists of a local change of either the dielectric constant, or the structural parameters. Within the plane of periodicity, the electromagnetic field is confined by the presence of a two-dimensional photonic band gap. When such a band gap is complete, the leakage within the plane can in principle be made arbitrarily small by increasing the number of periods of the crystal surrounding the defect. In the direction perpendicular to the high-index guiding layer, however, light will be able to leak out. The energy loss along this direction defines the radiation Q. It has been shown that such radiation Q can be improved by the use of a super defect, where the resonance modes are intentionally delocalized within the guiding layer in order to minimize the radiation losses in the vertical direction. Some have argued that high radiation Q in a two-dimensionally periodic photonic crystal slab geometry can be achieved by employing low index contrast-films in order to delocalize the resonant mode perpendicular to the guiding layer. Others have shown that the radiation Q can be improved by adjusting the dielectric constant in the defect region.